The investor titan converted 40 percent of his $1 billion equity short on Herbalife to less-risky long-term put options, according to a letter his Pershing Square hedge fund sent late Wednesday to investors, The Post has learned.

“The restructuring of the position preserves our opportunity for profit,” wrote Ackman in the letter, a copy of which was obtained by The Post.

“If [Herbalife] fails within a reasonable time frame we will make a similar amount of profit as if we had maintained the entire initial short position — while mitigating the risk of further substantial mark-to-market losses because our exposure on the put options is limited to the total premium paid.”

The move reduces the equity short to 12 percent from 16 percent of his $10.8 billion hedge-fund portfolio.

Ackman, who is seen as either resilient or obstinate depending on your point of view, clearly isn’t throwing in the towel, despite losses of about $500 million so far on his bet as the stock has surged 126 percent this year.

“While we have endured mark-to-market losses on this investment as Herbalife bulls have promoted the stock and downplayed the probability of government intervention, we believe it is only a matter of time before [it] is shut down and prosecuted by regulators,” he said in the letter.

Ackman, in the letter, maintains the bull case for Herbalife rests on lack of government action and a large buyback that would force him to cover, saying “the restructuring of our investment negates this important pillar of the bull case.”

The 47-year-old investor cast doubt on Herbalife’s ability to finance a buyback but also said “such a buyback would not require us to cover our position.”

In fact, a debt offering could allow Pershing Square to take a larger short against the company through the credit-default swap market, he said.

The long-dated, out-of-the money puts were privately negotiated with dealers at attractive prices given the surging stock price, Ackman said.